Both sides, who impressed in the last round, will be looking to secure an advantage at Philips Stadion ahead of the second leg of the European contest in Denmark on August 10.
PSV finished second behind Ajax in last season's Eredivisie, which saw them qualify for the second qualifying round of the Champions League, and they were handed a tough draw against Galatasaray.
In truth, though, the Dutch giants made light work of their Turkish opponents, running out 5-1 winners in the first leg on July 21 before recording a 2-1 victory in the second leg on July 28 to secure a 7-2 aggregate success, with Roger Schmidt's side breezing into the third qualifying round.
PSV have plenty to think about in the coming weeks, as they will take on Ajax in the Dutch Super Cup on August 7 before opening their 2021-22 league season against Hercales on July 14.
The Red and Whites simply cannot afford to take their eye off the ball in the Champions League, though, as they bid to make their way into the playoffs and then potentially the group stage.
PSV last competed in the group stage of the Champions League in 2018-19, when they finished bottom of Group B, having picked up just two points from their clashes with Barcelona, Tottenham Hotspur and Inter Milan.
Midtjylland, meanwhile, eliminated Celtic in the second qualifying round courtesy of a 2-1 victory over the Scottish giants in the second leg on July 28.
The two sides were level at 1-1 from the first leg in Glasgow, and they were also level at 1-1 after 90 minutes of the second leg on Wednesday night; Raphael Onyedika came up with a 94th-minute goal for Midtjylland, though, to secure a 2-1 win on the night and 3-2 aggregate success.
The Wolves played in last season's Champions League, finishing fourth in Group D, picking up just two points from their six matches against Liverpool, Ajax and Atalanta BC.
Bo Henriksen's side will be aware of the challenge that PSV could present, but they will enter this match off the back of three straight wins in all competitions, including a 2-0 success over Viborg in the league on Saturday.
Midtjylland are top of their domestic table with six points from their opening three matches, and they will follow Tuesday's European clash with their fourth league game of the season at home to Vejle on Friday.
PSV will be without the services of central defender Olivier Boscagli on Tuesday, as the 23-year-old received a red card against Galatasaray last time out, meaning that Nick Viergever could earn a spot in the side.
As for Midtjylland, Onyedika scored the decisive goal off the bench against Celtic in the last round, and there is a strong chance that the midfielder could now be handed a spot in the starting XI.
As mentioned, the Danish outfit were in league action on Saturday, and there will be changes to the side that took to the field for the two-goal victory over Viborg.
PSV Eindhoven possible starting lineup:
Drommel; Mwene, Ramalho, Viergever, Max; Sangare, Van Ginkel; Madueke, Gotze, Vertessen; Zahavi
We say: PSV Eindhoven 2-1 FC Midtjylland
Midtjylland are more than capable of overcoming PSV over two legs, but it is difficult to ignore the Dutch outfit's performance against Galatasaray in their last home fixture. We are expecting a tight first leg between two strong teams but believe that PSV will take an advantage into the second leg on August 10.
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